On uniqueness of recovering the convolution integro-differential operator from the spectrum of its non-smooth one-dimensional perturbation

Abstract

Abstract We consider a one-dimensional perturbation of the convolution integro-differential operator of arbitrary order on a finite interval. The inverse problem of recovering the convolution component from the spectrum is studied, provided that the perturbation term is known a priori. We prove the uniqueness theorem for this inverse problem and establish the minimal requirements on the perturbation term guarantying the informativity of the spectrum.

Keywords

• Integro-differential operator
• One-dimensional perturbation
• Convolution
• Inverse spectral problem